What kind of background I need to do graduate level research in Nanotechnology?

Not sure. Applied Sciences for most people probably. Did a quick google on such graduate level research and saw one for chemical engineering. Lots of different types of nanotechnology. We are still at ground level for so much of nanotechnology that one can take many paths, so use your intuition what you would most like to play around with. Lots of money is being poured into multiple directions by several countries. Natural science is good for getting a leg up on some arcane area, which is more likely to become a blind alley -- or all parties do not see what is really possible there, as is so common.

While I was in biotech once upon a time, what is called nanotechnology there can be really silly. This site suggests biotech as one path:

I am not sure, but you might try applied sciences since there is hesitation on your part. Your age is unknown to this thread, as well as previous studies. Also, there are other specialized areas like biotech, chemistry, etc. as well as natural science if you really get down to the small details. I would avoid the small details and try to see what appears to be happening, to mesh with what you really enjoy. Hence applied science, as hands on doing tends to increase enjoyment with most people, other than the bookish types which would likely already self answer the question by a quick google like I just did.

As for your situation I would consider the employment opportunities or lack there of in private industry, government or accademia.
Locally, versus nationally versus internationally.

I know someone who for reasons maternal allowed himself to be pushed into a field where there is nothing locally and whatever there is only located far afield. The only local is the few teaching positions where he is getting his degree.